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Model-independent mass determination of near-threshold states from short-range production

Yong-Hui Lin, Hans-Werner Hammer, Ulf-G. Meißner

Abstract

We propose a novel observable for the precision measurements of a wide class of near-threshold dimer states: the short-range production rate of a dimer--spectator two-body system, composed of the given near-threshold state and one of its constituents. Within the framework of nonrelativistic effective field theory, these production rates exhibit characteristic line shapes for the specific partial wave and reach a model-independent minimum. This feature enables a precise extraction of their masses from experimental data, provided that the line shape can be resolved with sufficient accuracy. Applying this novel method to both the $T_{b\bar{b}1}(10610)B$ and $T_{b\bar{b}1}(10650)B^*$ systems allows for a precise determination of the binding energy $δ$ of the $T_{b\bar{b}1}(10610)$ and $T_{b\bar{b}1}(10650)$ via the relation of $δ=-{E_{\text{dip}}^{\text{exp}}}/{0.1983}$ once the respective dip position $E_{\text{dip}}^{\text{exp}}$ is experimentally identified.

Model-independent mass determination of near-threshold states from short-range production

Abstract

We propose a novel observable for the precision measurements of a wide class of near-threshold dimer states: the short-range production rate of a dimer--spectator two-body system, composed of the given near-threshold state and one of its constituents. Within the framework of nonrelativistic effective field theory, these production rates exhibit characteristic line shapes for the specific partial wave and reach a model-independent minimum. This feature enables a precise extraction of their masses from experimental data, provided that the line shape can be resolved with sufficient accuracy. Applying this novel method to both the and systems allows for a precise determination of the binding energy of the and via the relation of once the respective dip position is experimentally identified.

Paper Structure

This paper contains 2 sections, 10 equations, 5 figures, 1 table.

Table of Contents

  1. Supplemental Material
  2. Effective-range corrections to point production

Figures (5)

  • Figure 1: Diagram for the point production of the dimer-spectator pair.
  • Figure 2: Variation of the $S$-wave point production rate with the mass ratio $r$ (left) for the $Z_b B$ system with $(S, I)=(1,3/2)$ and the position $x_{\rm dip}$ of the characteristic dip as a linear function of $r$ (right).
  • Figure 3: Variation of the $S$-wave point production rate with the quantum number factor $C_{SI}$. The characteristic peak-dip structure only appears when $4/12<C_{SI}<7/12$ for $r=1$.
  • Figure 4: The point production rates for the $Z_b B$ system with $(S, I)=(1,3/2)$ under the assumption that the $Z_b$ is a dimer state composed of $B^*\bar{B}$-$B\bar{B}^*$ with positive binding energy. The total point production rate exhibits a dip at $x=0.8022$, shown as the vertical dashed line in the left panel.
  • Figure 5: Dip position $x_{\text{dip}}$ versus mass ratio $r$ for various $\rho\gamma$. Symbols indicate explicit solutions of Eq. \ref{['eq: inteq0NL1']} while lines show linear fits.